Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2025 May 21;31(6):165.
doi: 10.1007/s00894-025-06395-8.

QTAIM view of Ru-Ru bonding in a series of tri-ruthenium hydride clusters: [{CpRu(μ-H)}3(μ3-BH)], [{CpRu(μ-H)}3(μ3-H)2], [{CpRu(CO)}3(μ-BO)(μ-H)2], and [{CpRu(μ-H)}3(μ3-AlEt)]

Noorhan Ali Hamza  1 , Haider Ali Hamza  2 , Muhsen Abood Muhsen Al-Ibadi  3   4 , Emad Salaam Abood  5 , Ali R Khudhair  6
Affiliations

QTAIM view of Ru-Ru bonding in a series of tri-ruthenium hydride clusters: [{CpRu(μ-H)}3(μ3-BH)], [{CpRu(μ-H)}3(μ3-H)2], [{CpRu(CO)}3(μ-BO)(μ-H)2], and [{CpRu(μ-H)}3(μ3-AlEt)]

Noorhan Ali Hamza et al. J Mol Model. .

Abstract

Context: The ruthenium-ruthenium and ruthenium-ligand bonding interactions in the [{CpRu(μ-H)} 3(μ3-BH)](1), [{CpRu(μ-H)}3(μ3-H)2](2), [{CpRu(CO)}3(μ-BO)(μ-H)2](3), and [{CpRu(μ-H)}3(μ3-AlEt)](4) clusters were examined using density functional theory (DFT). Various parameters related to electron density, including the electron density ρ(b), Laplacian ∇2ρ(b), local energy density H(b), local kinetic energy density G(b), potential energy density V(b), and bond delocalization index (A, B), were calculated using the quantum theory of atoms in a molecule (QTAIM). Other QTAIM indicators, such as the electron localization function (ELF) and source function (SF) were computed. According to the transition metal complexes referenced in the academic literature, the computed topological parameters are consistent. The calculated data have made it possible to compare the topological characteristics of related but distinct atom-to-atom interactions, including Ru-H interactions against Ru-BH, Ru-BO, and Ru-Al interactions, as well as H-bridged Ru-Ru interactions versus BH-, BO-, and Al-bridged interactions. The electron density distribution of the Ru-Ru interactions is influenced by different bridging ligands. Despite the presence of bridged hydride and boron in clusters 1 and 3, H in cluster 2, and H and Al in the Ru-Ru interactions of 4, no localized bond, bond critical, or bond path was observed. However, the large delocalization indices δ(Ru, Ru) indicate that significant indirect Ru-Ru interactions are mediated through bridging ligands. For clusters 1, 2, 3, and 4, we propose the following interactions for their core components: H3-Ru-B (7c-14e), H5-Ru (8c-12e), H2-Ru3-B (6c-8e), and H3-Ru3-Al (7c-14e). The AdNDP analysis confirms the presence of 4c-2e multicenter bonds in several Ru₃-based clusters, emphasizing the critical role of electron delocalization in stabilizing their core structures. The BO ligand has a higher delocalization index of 1.023, indicating that it shares a pair of electrons. Moreover, the delocalization index for cluster 3, δ(Ru…OCO), is very large at 0.576. This suggests that CO ligands play a significant role in M π-back-donation.

Methods: Using the PBE1PBE hybrid functional and an effective core potential LanL2DZ basis set for the atoms of Ru as well as the all-electron 6-31G(d) basis set for the other atoms (Al, B, H, C and O), the optimizations were performed using the Gaussian 09 program. The geometries were verified as a local minimum by examining if imaginary vibrational frequencies were present after unrestricted optimization was carried out. Utilizing AIM2000 and Multiwfn software, we conducted QTAIM analysis, incorporating PBE1PBE/WTBS for the Ru atoms. 6-31G(d,p) and 6-311 + + G(3df,3pd) were the basis set for the atoms of Al, B, H, C and O. Moreover, we employed the SF and ELF.

Keywords: AdNDP analysis; DFT calculations; ELF; Electron density; QTAIM; Topological properties; Transition metal.

PubMed Disclaimer

Conflict of interest statement

Declarations. Competing interests: The authors declare no competing interests. Ethical approval: Not applicable.

References

    1. Al-Ibadi MA, Duckett SB, McGrady JE (2012) Characterisation of tri-ruthenium dihydride complexes through the computation of NMR parameters. Dalton Trans 41(15):4618–4625. https://doi.org/10.1016/j.ica.2015.05.002 - DOI - PubMed
    1. Hogarth G, Kabir SE, Nordlander E (2010) Cluster chemistry in the Noughties: new developments and their relationship to nanoparticles. Dalton Trans 39(27):6153–6174. https://doi.org/10.1039/c000514b - DOI - PubMed
    1. Muetterties EL (1977) Molecular metal clusters: cluster chemistry may provide valuable insights to chemisorption and catalysis on surfaces. Science 196(4292):839–848. https://doi.org/10.1126/science.196.4292.839 - DOI - PubMed
    1. Guzman-Jimenez IY, van Hal JW, Whitmire KH (2003) Metal cluster catalysis: a kinetic and mechanistic study of the carbonylation of methanol to give methyl formate as catalyzed by [Et4N] 2 [Fe3 (CO) 9E](E= S, Se, Te). Organometallics 22(9):1914–1922. https://doi.org/10.1021/om020548+ - DOI
    1. Böhme DK, Schwarz H (2005) Gas-phase catalysis by atomic and cluster metal ions: the ultimate single-site catalysts. Angew Chem Int Ed 44(16):2336–2354 - DOI

LinkOut - more resources